A numerical technique to increase the stability of the ADI method in solidification simulation

摘要

Simulation of solidification is based on solving the heat conduction equation, a well-known partial differential equation. Among the various numerical methods which exist to solve this equation, a finite-difference method called the Alternating Direction Implicit (ADI) variant has been used in the present research. While this method is known for its unconditional stability, problems may arise in practice. During the initial stages of the simulation, discontinuous temperature distributions may be calculated which cannot exist in reality. The cause of the deteriorated temperature distribution is explained and is illustrated in a real casting configuration. A new numerical technique is described which overcomes these problems. Practical simulation results illustrate the benefits of the method.